TV REVIEW Leonardo plays Sherlock

THE ONE WHERE Suffering intense dreams about the man he saw hanged in the town square, Leonardo has the body exhumed and embarks on an elaborate quest to work out who he was and his connection to the Turk – all while trying to get the machine gun he's promised Lorenzo functioning properly. There's also the small matter of an unpleasant visitor from the Vatican...

VERDICT Having spent its first episode more preoccupied with introducing its hero than telling a story, Da Vinci's Demons gets stuck into some serious arc-building this week. It turns out that there's more to the hanged man than initially met the eye, so Leonardo turns detective to get to the bottom of a mystery that ties into the Sons of Mithras and the Book of Leaves. It's a hell of a lot of fun, a rip-roaring adventure tale that's as much Da Vinci Code (in a good way) as it is Da Vinci history lesson.

Da Vinci, who can seemingly do anything he puts his mind to, has a pretty good shot at impersonating Sherlock Holmes with his powers of deduction, making nigh-on impossible leaps of logic as he discovers half a key in a dead man's stomach, and then a book among thousands in a library. It's thoroughly ridiculous stuff, but delivered with such a winning sense of adventure that it's easy to forgive the implausibility.

Meanwhile, Leonardo discovers that working for the Medicis isn't all fun and games – not least because his dad, of all people, wrote a clause into his contract stating that failure to deliver a functioning weapon would be classed as fraud, an offence punishable by death. Da Vinci's backfiring prototypes reveal Lorenzo to be one of the show's more intriguing characters: surprisingly patient and tolerant of Leonardo's schemes, yet happy to rattle the artisan when he needs to. Their final encounter, after Da Vinci has explosively pledged his allegiance to Florence, suggests that theirs could be a relationship of mutual respect and gain. As long as Lorenzo doesn't find out about his mistress Lucrezia's fling with Leonardo, of course...

Having looked totally in control of matters last week, Lucrezia seems slightly out of her depth when faced with a Count Riario on a business trip to Florence – he's the one holding all the cards in their arrangement. Just a bit part player in episode one, Riario turns out to be a tremendous villain here – slightly pantomime, yes, but the way he schemes and tortures people with relish suggests that he could be a baddie we love to hate. But what does he want with that key?

WHO GOES THERE Anyone else think that the quarry-like hole in the ground where Da Vinci bests Riario could have been lifted straight out of ’70s/’80s Doctor Who ?

TRIVIA Each episode of the series is named after a tarot card. Last week we saw " The Hanged Man ", this week is "The Serpent", and following episodes will be "The Prisoner", "The Magician", "The Tower", "The Devil", "The Hierophant" and "The Lovers".

TRIVIA 2 David Goyer's co-writer on this episode is Scott M Gimple, the new showrunner on The Walking Dead .

SPECULATION After last week's revelation that Lucrezia is Riario's spy in the Florentine court, it's now obvious that the pair don't share a happy professional relationship. It looks like Lucrezia is working for Rome under duress – is Riario blackmailing her in some way?

DA VINCI VISION Leonardo's in-vision diagrams are used much more effectively here than they were last week, particularly when his mind reveals the workings of a lock. When Da Vinci uses his unique way of looking at the world to assess the structure of a building before using a pulley to escape to freedom, however, it's effectively working as a superpower. You can take David Goyer out of the superhero movie, but you can't take the superhero movie out of David Goyer...

OUCH! Count Riario's Widow's Tear torture device is a rather unpleasant piece of kit, scratching skin off the back of the victim's hand with a diamond, one layer at a time. We'll pass, thanks.

MAKING HISTORY The real Da Vinci was one of the leading anatomists of his time, so it really isn't far-fetched that he should know his way around a dissection. He was also a skilled engineer who designed machines to defend the city – initially Florence, later Venice.

Also, Leonardo and co wouldn't recognise the map of South America because for them it's yet to be discovered – going on Da Vinci's date of birth (1452) and his rough age in the show (late 20s), the series must be set around 1480. Columbus didn't set sale for the New World until 1492.

CLARICE AND PRESENT DANGER We actually got to hear Lorenzo's wife Clarice speak this week, but she's still very much a background player. Expect to see more from her as the series develops.

IT'S WOTSISNAME Florentine law enforcement officer Black Martin is played by Tim Faraday, who you might recognise as Helen Cutter's clone army in Primeval .

BEST LINE Riario: Da Vinci has the key. Why would he concern himself with a bookshop? Lucrezia: I don't know. Perhaps Da Vinci is more clever than you. But then that would be heresy, wouldn't it?